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Primary 5 Mathematics Geometry Quiz

Free P5 Maths Geometry quiz, Ox Exam version, with questions, answers, and syllabus-aligned practice for Singapore students.

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Primary 5 Mathematics From Real Exams Generated by Ox Alpha Updated 2026-08-27

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Questions

Primary 5 Mathematics Quiz - Geometry

Name: ______________________ Class: ____________ Date: ______________

Duration: 60 minutes Total Marks: 70 Score: __________ / 70

Instructions:

Answer ALL 20 questions.
Show your working clearly. Marks are awarded for correct method as well as final answers.
Include units ( $^\circ$ , cm, cm $^2$ , cm $^3$ , $\ell$ , ml) in your final answers.
Diagrams are not drawn to scale.
For multiple-choice questions, write the option number (1), (2), (3) or (4) in the answer space.

Section A: Multiple Choice (Questions 1–5, 2 marks each)

Question 1.

Three angles meet at a point. Two of the angles are $148^\circ$ and $95^\circ$ . What is the size of the third angle?

(1) $107^\circ$ (2) $117^\circ$ (3) $127^\circ$ (4) $137^\circ$

Answer: ____________ [2]

Question 2.

Straight lines $PQ$ and $RS$ intersect at point $T$ . Angle $PTR = 68^\circ$ . What is the size of angle $QTS$ ?

(1) $22^\circ$ (2) $68^\circ$ (3) $112^\circ$ (4) $122^\circ$

Answer: ____________ [2]

Question 3.

A triangle has interior angles of $40^\circ$ , $40^\circ$ and $100^\circ$ . What type of triangle is it?

(1) Equilateral (2) Isosceles (3) Right-angled (4) Scalene

Answer: ____________ [2]

Question 4.

$WXYZ$ is a rhombus. One of its angles is $65^\circ$ . What is the size of the angle opposite to it?

(1) $25^\circ$ (2) $65^\circ$ (3) $115^\circ$ (4) $155^\circ$

Answer: ____________ [2]

Question 5.

Angle $x$ and an angle of $112^\circ$ lie on a straight line. What is the value of $x$ ?

(1) $48^\circ$ (2) $58^\circ$ (3) $68^\circ$ (4) $78^\circ$

Answer: ____________ [2]

Section B: Short Answer (Questions 6–10, 3 marks each)

Question 6.

In the figure, $AOB$ is a straight line. Angle $AOC = 35^\circ$ and angle $COD = 90^\circ$ . Find angle $DOB$ .

Image pending generation: diagram for Q6.

Working space:

Answer: ____________ [3]

Question 7.

Triangle $XYZ$ is an isosceles triangle with $XY = XZ$ . The vertex angle $YXZ = 40^\circ$ . Find the size of each base angle ( $\angle XYZ$ and $\angle XZY$ ).

Working space:

Answer: ____________ [3]

Question 8.

$PQRS$ is a parallelogram. Angle $P = 115^\circ$ . Find the sizes of angle $Q$ , angle $R$ and angle $S$ .

Working space:

Answer: ____________ [3]

Question 9.

(a) A triangular sail has a base of $12$ cm and a perpendicular height of $8$ cm. Find its area. [1]

(b) Another triangle has the same area as the sail in (a) but a base of $16$ cm. Find its perpendicular height. [2]

Working space:

Answers: (a) ____________ (b) ____________ [3]

Question 10.

Four angles meet at a point. Their sizes are $x^\circ$ , $2x^\circ$ , $3x^\circ$ and $30^\circ$ . Find the value of $x$ .

Working space:

Answer: ____________ [3]

Section C: Structured Questions (Questions 11–15, 4 marks each)

Question 11.

$ABCD$ is a trapezium with $AB$ parallel to $DC$ . Angle $DAB = 72^\circ$ and angle $BCD = 115^\circ$ .

(a) Find angle $ADC$ . [2]

(b) Find angle $ABC$ . [2]

Working space:

Answers: (a) ____________ (b) ____________ [4]

Question 12.

The figure shows a composite shape made of a rectangle with an isosceles triangle sitting on top of it. Find the total area of the shape.

Image pending generation: diagram for Q12.

Working space:

Answer: ____________ [4]

Question 13.

A rectangular tank measures $25$ cm by $12$ cm. It contains water to a depth of $8$ cm.

(a) Find the volume of water in the tank in cm $^3$ . [2]

(b) Express the volume of water in litres and millilitres. [2]

Working space:

Answers: (a) ____________ (b) ____________ [4]

Question 14.

In the figure, straight lines $AB$ and $CD$ intersect at point $O$ . Angle $AOC = 55^\circ$ .

Image pending generation: diagram for Q14.

(a) Find angle $BOD$ . Explain which angle property you used. [2]

(b) Find angle $AOD$ . Show your working. [2]

Working space:

Answers: (a) ____________ (b) ____________ [4]

Question 15.

A wooden cube has edges of $6$ cm.

(a) Find the volume of the cube. [2]

(b) Small cubes of edge $2$ cm are cut from the large cube. How many small cubes can be made? [2]

Working space:

Answers: (a) ____________ (b) ____________ [4]

Section D: Problem Solving (Questions 16–20, 5 marks each)

Question 16.

In triangle $DEF$ , angle $E = x^\circ$ , angle $D = 3x^\circ$ and angle $F = 48^\circ$ .

(a) Form an equation and find the value of $x$ . [2]

(b) Find angle $D$ and angle $E$ . [1]

Working space:

Answers: (a) ____________ (b) ____________ (c) ____________ [5]

Question 17.

$ABCD$ is a rhombus with angle $ADC = 104^\circ$ . The diagonal $BD$ is drawn inside the rhombus.

(a) Explain why angle $DAB = 76^\circ$ . [1]

(b) Explain why triangle $ABD$ is an isosceles triangle, and find angle $ADB$ . [2]

Working space:

Answers: (a) ____________ (b) ____________ (c) ____________ [5]

Question 18.

An empty rectangular tank has a base measuring $30$ cm by $20$ cm and a height of $15$ cm.

(a) Find the capacity of the tank in cm $^3$ . [1]

(b) The tank contains water to a depth of $10$ cm. Find the volume of water in litres. [2]

Working space:

Answers: (a) ____________ (b) ____________ (c) ____________ [5]

Question 19.

In the figure, straight lines $AB$ and $CD$ intersect at point $O$ . Ray $OE$ lies between $OC$ and $OB$ . Angle $AOC = 65^\circ$ and angle $COE = 40^\circ$ .

Image pending generation: diagram for Q19.

(a) Find angle $BOD$ . [1]

(b) Find angle $EOB$ . Show your working. [2]

Working space:

Answers: (a) ____________ (b) ____________ (c) ____________ [5]

Question 20.

A rectangular tank measures $40$ cm by $25$ cm by $20$ cm. It contains water to a depth of $18$ cm. A metal cube of edge $10$ cm is then placed inside the tank.

(a) Find the volume of water in the tank in cm $^3$ . [1]

(b) Find the volume of the cube in cm $^3$ . [1]

(d) Will the water overflow from the tank? Explain your answer. [1]

Working space:

Answers: (a) ____________ (b) ____________ (c) ____________ (d) ____________ [5]

End of Quiz

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Answers

Primary 5 Mathematics Quiz - Geometry: Answer Key

Answer 1.

$360^\circ - 148^\circ - 95^\circ = 117^\circ$ . Correct option: (2).

Answer 2.

Vertically opposite angles are equal, so angle $QTS = 68^\circ$ . Correct option: (2).

Answer 3.

Two angles are equal ( $40^\circ$ each), so two sides are equal: isosceles. Correct option: (2).

Answer 4.

Opposite angles of a rhombus are equal, so the answer is $65^\circ$ . Correct option: (2).

Answer 5.

$x = 180^\circ - 112^\circ = 68^\circ$ . Correct option: (3).

Answer 6.

Angles on a straight line add to $180^\circ$ : $x = 180^\circ - 35^\circ - 90^\circ = 55^\circ$ .

Answer 7.

Base angles are equal. Each base angle $= (180^\circ - 40^\circ) \div 2 = 140^\circ \div 2 = 70^\circ$ .

Answer 8.

Adjacent angles of a parallelogram are supplementary and opposite angles are equal: angle $Q = 180^\circ - 115^\circ = 65^\circ$ ; angle $R = 115^\circ$ ; angle $S = 65^\circ$ .

Answer 9.

(a) Area $= \frac{1}{2} \times 12 \times 8 = 48$ cm $^2$ . (b) Height $= (2 \times 48) \div 16 = 96 \div 16 = 6$ cm.

Answer 10.

$x + 2x + 3x + 30 = 360$ , so $6x = 330$ and $x = 55$ .

Answer 11.

(a) $AB \parallel DC$ , so angle $ADC$ and angle $DAB$ are co-interior: $ADC = 180^\circ - 72^\circ = 108^\circ$ . (b) Angle $ABC$ and angle $BCD$ are co-interior: $ABC = 180^\circ - 115^\circ = 65^\circ$ .

Answer 12.

Rectangle: $10 \times 6 = 60$ cm $^2$ . Triangle: $\frac{1}{2} \times 10 \times 4 = 20$ cm $^2$ . Total area $= 60 + 20 = 80$ cm $^2$ .

Answer 13.

(a) Volume $= 25 \times 12 \times 8 = 2400$ cm $^3$ . (b) $2400$ cm $^3 = 2\,\ell\,400$ ml.

Answer 14.

(a) Angle $BOD = 55^\circ$ because vertically opposite angles are equal. (b) Angle $AOD = 180^\circ - 55^\circ = 125^\circ$ (angles on the straight line $AB$ add to $180^\circ$ ).

Answer 15.

(a) Volume $= 6 \times 6 \times 6 = 216$ cm $^3$ . (b) Small cube volume $= 2 \times 2 \times 2 = 8$ cm $^3$ ; number $= 216 \div 8 = 27$ small cubes.

Answer 16.

(a) $x + 3x + 48 = 180$ , so $4x = 132$ and $x = 33$ . (b) Angle $D = 3 \times 33 = 99^\circ$ ; angle $E = 33^\circ$ . (c) By angles: obtuse triangle, since one angle ( $99^\circ$ ) is greater than $90^\circ$ . By sides: scalene triangle, since all three angles are different, so all three sides are different.

Answer 17.

(a) Adjacent angles of a rhombus are supplementary: $DAB = 180^\circ - 104^\circ = 76^\circ$ . (b) $AB = AD$ (all sides of a rhombus are equal), so triangle $ABD$ is isosceles. Thus angle $ADB =$ angle $ABD = (180^\circ - 76^\circ) \div 2 = 52^\circ$ . (c) Angle $ABD = 52^\circ$ (equal to angle $ADB$ , shown in (b)).

Answer 18.

(a) Capacity $= 30 \times 20 \times 15 = 9000$ cm $^3$ . (b) Water volume $= 30 \times 20 \times 10 = 6000$ cm $^3 = 6\,\ell$ . (c) Water needed $= 9000 - 6000 = 3000$ cm $^3$ .

Answer 19.

(a) Angle $BOD = 65^\circ$ (vertically opposite angle $AOC$ ). (b) Angle $BOC = 180^\circ - 65^\circ = 115^\circ$ (straight line $CD$ ), so angle $EOB = 115^\circ - 40^\circ = 75^\circ$ . (c) No. Angle $EOB = 75^\circ \neq 90^\circ$ (equivalently angle $AOE = 65^\circ + 40^\circ = 105^\circ \neq 90^\circ$ ), so $OE$ is not perpendicular to $AB$ .

Answer 20.

(a) Volume of water $= 40 \times 25 \times 18 = 18\,000$ cm $^3$ . (b) Volume of cube $= 10 \times 10 \times 10 = 1000$ cm $^3$ . (c) Total volume $= 18\,000 + 1000 = 19\,000$ cm $^3$ ; new depth $= 19\,000 \div (40 \times 25) = 19\,000 \div 1000 = 19$ cm. (d) No. The new depth of $19$ cm is less than the tank height of $20$ cm, so the water does not overflow.